%
%this is a method of lines solution of the 1d heat equation
%
%  u_t = u_xx
%  u=0 at x=0,1
%  u=f(x)=sin(pi x) at t=0
%
% (DMA, 5-29-08)
%
% This code also generates a movie (an avi file).   Sometimes
% problems can arise with the generation of the avi file if
% Matlab encounters an error during the running of the code.
% Don't expect this code to be foolproof!!
%*******************************************************
clear all;
N=50;
%define boundary values
a=0;
b=1;
ua=0;
ub=0;
% boundary interval
dx =(b-a)/N;
x = linspace(a,b,N+1);
%
uinit  = sin(pi*x);
uin= uinit(2:N);
tinit  = 0;
tfinal = 10;
tspan = [tinit tfinal];
%
RelTolVal=10^(-4);
AbsTolVal=10^(-6);
options = odeset ('RelTol',RelTolVal,'AbsTol',AbsTolVal);
%
[t,u]  = ode23s (@heat_mol_RHS, tspan, uin,options, N,dx,ua,ub);
%
%[row, col] = size(u);
%
%
% Movie
%
kframes = size(t);

Frame = moviein(kframes);
mov = avifile('heat_mol.avi','quality',100,'fps',5);
for k = 1:kframes      
    plot(x,[ua u(k,:) ub],'b');hold on;
    grid on;
    xlabel('Spatial x');
    ylabel('u(x,t)');
    axis([0,1,-0.08,1.0]);
    hold off
    Frames(:,k) = getframe;
    F = getframe;
    mov = addframe(mov,F);
end
movie(Frames,3,20);   % movie(nameofmovie,# of times played, # of frames per second)
mov=close(mov);